A sphere of mass 
is suspended by a thread of length ' 
' is oscillating in a vertical
plane, the angular amplitude being 
. What is the tension in the thread when it makes an angle 
with the vertical during oscillations? If the thread can support a maximum tension of 2 mg , then what can be the maximum angular amplitude of oscillation of the sphere without breaking the rope?
Text Solution
Verified by ExpertsA
Apply Newton ’ s law at angle θ
T – mg cos θ = 
...
apply energy conservation from θ 0 to θ
mg λ (cos θ – cos θ 0 ) = 
mv 2 ...
From and
T = 3mg cos θ – 2mg cos θ 0 ....
T max = 2mg (put in equation )
⇒θ 0 = 60º
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